SPURIOUS CORRELATION AND IT'S DETECTION

Although statisticians warn against the flaw of spurious correlation, little or nothing is suggested as to how to identify its presence other than to critically examine the conclusions. In cross-sectional analysis, the phenomena of spurious correlation can be observed by injecting structure by creating ratios with a common denominator.

Early authors like Bartlett (1931) asked "Why do we sometimes get spurious correlation between time series". The presence of ARIMA structure usually reflects omitted input series or incorrect lag structures. Time series analysts who correctly augment their model with ARIMA structure can and do expose the spurious nature of a candidate input. This is demonstrated in the Australian Wine Study. Spurious correlation induced by omitted Intervention series is exposed in the Demand For Gas Study.

The concept of incorporating needed but omitted variables is clear in time series because the concomitant variable is usually obvious after its presence has been detected via ARIMA structure with a conclusion that the X variable is not significant above and beyond the historical impact of Y. There are many cases where the ARIMA structure , having reduced the error variance enables a clearer picture and the significance of a candidate variable. The Income/Consumption study illustrates this rather nicely. This process of identification usually arises when conclusions are drawn like "fireman cause damage" or "storks bring babies" or "the number of words in a person's vocabulary depends on their foot size" or "beer is a snob good because actual price was used rather than real price.".

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